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SDEs with two reflecting barriers driven by optional processes with regulated trajectories

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  • Falkowski, Adrian

Abstract

We study the existence, uniqueness, and approximation of solutions of general stochastic differential equations (SDEs) with two time-dependent reflecting barriers driven by optional semimartingales. We do not assume that the probability space has to satisfy the usual conditions. We define and solve an appropriate version of the deterministic Skorokhod problem for regulated functions. Applications to currency option pricing in financial models are given.

Suggested Citation

  • Falkowski, Adrian, 2025. "SDEs with two reflecting barriers driven by optional processes with regulated trajectories," Stochastic Processes and their Applications, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:spapps:v:179:y:2025:i:c:s0304414924002175
    DOI: 10.1016/j.spa.2024.104509
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